Giorgio Gilestro
62c68d6c8c
Enter the Lamarckian society with a robust theoretical frame. The single-
locus, fixed-p* model can only express recovery toward a ceiling; the
society's load-bearing claim is vertical -- capability that EXCEEDS any
component. Generalize knowledge to a distribution over genotypes (L
biallelic loci, K=2^L, additive fitness = # correct loci), reusing all the
K-mode machinery. The one new operator is recombination: free recombination
sends p -> product of per-locus marginals (linkage equilibrium).
E8 (star, kind: society) -- the vertical claim / Fisher-Muller: decorrelated
PARENTS (specialists, expert on their loci, agnostic elsewhere) are
recombined; sexual merge assembles a genotype fitter than any parent,
climbing to the optimum (12/12, a genotype no parent had) as parent count
grows and rho->0, while the best single parent (~8.7) and the mean-mixture
"model soup" (~11.6) plateau below. Reuses make_retention_matrix (locus
mastery replaces tail-item retention).
E7 (kind: genotype_lineage) -- the advantage of sex: a single population
adapts toward the optimum; the sexual lineage adapts faster than asexual
(clonal interference) by keeping loci in linkage equilibrium (LD->0 vs LD
spike). Honest scope: a speed advantage, not a permanent Muller's-ratchet
gap (subtle to force); E8 carries the headline.
Metaphor shift (per GG): the society is sexual reproduction with UNBOUNDED
parents, not teacher->pupil. Teacher->pupil caps at the ceiling; n-parent
recombination is combinatorial and generative, and unlike biology there is
no two-parent limit. Collapse = asexual degradation; the cure = sex. This
unifies E4 (merge != average) + E6 (irreversibility) under evolution-of-sex
theory and reaches ground Riis's single-locus n-grams cannot.
New: knowledge/{genotype,genotype_lineage,society}.py, configs/layer1/{E7,
E8}.yaml, figures/plot_{E7,E8}.py, READMEs, tests/test_genotype.py (+7).
experiment.py dispatch (kind in {genotype_lineage, society}); make layer1
wired. 112 tests green.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
2.3 KiB
E7 — the advantage of sex: recombination adapts faster than clonal reproduction
Claim tested. The dynamic mechanism behind E8: why can a recombining society reach capability a lone lineage cannot? Because recombination reassorts beneficial variants that arise in different sub-lineages, while an asexual (clonal) lineage suffers clonal interference — the variants compete and cannot combine.
Setup. A single population (distribution over 2^L genotypes, L=12) adapts from all-wrong
toward the multi-locus optimum under the composed step: selection (fitness-proportional) + drift
(resample n=150) + mutation (per-locus flips, μ=0.02) + recombination. Two arms — asexual
(recomb_rate=0) vs sexual (recomb_rate=1). 20 replicates.
Symbols
- asexual/clonal = offspring are whole-genotype copies (Layer-1's regime) · sexual = loci reassorted across the population each generation.
- fitness = number of correct loci (optimum =
L) · linkage disequilibrium |D| = how far the loci are from statistical independence (correct alleles scattered across different genotypes).
The two panels
- Advantage of sex. Mean fitness over generations: the sexual lineage (red) climbs faster than the asexual one (grey) through the adaptation phase (gen ~10–35). Honest scope: both plateau near the optimum by gen ~40 in this tractable regime — this is a speed advantage, not a permanent gap (the single-population Muller's ratchet is subtle to force; E8 carries the headline).
- Mechanism. Linkage disequilibrium over generations: the asexual lineage spikes to
|D|≈0.04during adaptation (beneficial alleles held apart, scattered across genotypes), while the sexual lineage stays at|D|≈0— it assembles them. The LD gap is exactly why sexual adapts faster.
Takeaway
Recombination's advantage is real and classical: it combines good ideas that arose independently, which clonal reproduction cannot. This is the population-level reason a single evolving model lineage degrades or stalls where a recombining society climbs — and it grounds the E8 vertical result in the evolution-of-sex theory. Falsifier (not triggered): if the sexual lineage adapted no faster than the asexual one (and kept the same LD), recombination would do no work.